#     ## 4.3.5 Determining the Class Precedence List

The defclass form for a class provides a total ordering on that class and its direct superclasses. This ordering is called the local precedence order. It is an ordered list of the class and its direct superclasses. The class precedence list for a class C is a total ordering on C and its superclasses that is consistent with the local precedence orders for each of C and its superclasses.

A class precedes its direct superclasses, and a direct superclass precedes all other direct superclasses specified to its right in the superclasses list of the defclass form. For every class C, define

RC={(C,C1),(C1,C2),...,(Cn-1,Cn)}

where C1,...,Cn are the direct superclasses of C in the order in which they are mentioned in the defclass form. These ordered pairs generate the total ordering on the class C and its direct superclasses.

Let SC be the set of C and its superclasses. Let R be

R=Uc<ELEMENT-OF>SCRc

.

The set R might or might not generate a partial ordering, depending on whether the Rc, c<ELEMENT-OF>SC, are consistent; it is assumed that they are consistent and that R generates a partial ordering. When the Rc are not consistent, it is said that R is inconsistent.

To compute the class precedence list for C, topologically sort the elements of SC with respect to the partial ordering generated by R. When the topological sort must select a class from a set of two or more classes, none of which are preceded by other classes with respect to R, the class selected is chosen deterministically, as described below.

If R is inconsistent, an error is signaled.

## 4.3.5.2 Examples of Class Precedence List Determination      